Question

Please provide steps and explanations. Thank you!

Dr. M is trying to form a debate team from students in his class. A class of 15 students has eight 2nd-year students and the rest are 1st-years. How many ways can Dr.M form a debate team consisting of four 2nd-years and two 1st-years?

Answer 1

solution:

Given that

Total No.of students = 15

No.of 2nd-year students = 8

No.of 1st-year students = 15 -8 = 7

2 2 2 2 2 2 2 2

1 1 1 1 1 1 1

8 students 7 students

Also,Given that

Dr.M wants to form a debate team consisting of four 2nd year and two 1st year

Step-1: Dr.M wants to select 4 students from 2nd year students

So, No.of ways he can select 4 students from 8 - 2nd year students = 8C4 = 70

Step-2 : Dr.M wants to select 2 students from 1st year students

So,No.of ways he can select 2 students from 7 - 1st year students = 7C2 = 21

Total No.of ways that Dr.M can form a debate Team = 70 * 21 = 1470